The common basis of the theories of linear cyclic methods and Runge-Kutta methods Original Research Article

This contribution is a survey of results on general linear methods. Both classical theories, Dahlquistʹs theory of multistep methods as well as Butcherʹs theory of Runge-Kutta methods, are extended in such a way that a common notation and uniform concepts become possible. The distinction between linear and nonlinear methods for ODEs vanishes in favour of a common approach to different types of (composite) linear methods.